HW 5 Extra: Statistical Analysis and Uncertainties Problem 1 (10 points) Multiple source errors into total error (50 points) The mass of three objects are measured using three different scales. The measured mass of each object is: 40.1 kg, 8.5 0.5 kg, and 735 1g. 1. What is the value of the uncertainty in the total mass? 2. Report the total mass value with the total uncertainty. Problem 2 (15 points) Temperature measurements of the exterior of a house resulted in the following data (in F). 78.81, 78.56, 75.89, 77.09, 76.19, 77.80, 76.38, 75.82, 77.27, 77.39, 77.65, 76.89, 76.25, 76.33, 76.99, 75.99, 76.85, 75.26, 76.56, 75.68, 77.07, 75.40, 76.38, 75.42, 76.88 1. Calculate the minimum, maximum, mean, variance and standard deviation of the temperature. (10 points) 2. Report the most probable temperature with its associated error. (10 points) Problem 3 (15 points) In a factory producing mechanical components 1000 components were measured and statistical analysis resulted in the following table Each listed item is 3 points. 1. What is a width of statistical class? 2. Do number of classes correspond to estimate using a Sturgis Rule? 3. Plot histogram of data. Does it match Gaussian (Normal distribution)? 4. What is your estimate of mean from the plot? 5. Consider standard deviation of a sample is 7.4837e-05. What is the standard error of the data? How many significant digits do we keep in standard error estimate? Problem 4 (10 points) Significant digits. Round the following measurement result where the first number is measurement mean and the second number is measurement error. Statistical Class Frequency of midpoint (inches) occurrence 0.512 5 0.519 38 0.526 130 0.533 184 0.540 200 0.547 175 0.554 155 0.561 73 0.568 32 0.575 8 Rounded result Measurement result (a) 7679.555 (b) (5.6250.0444)-10-3 (c) 18.34287 0.02675 (d) 6.330.0547 (e) 7.3990.098 Points 2 2 2 2 2